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Concepts Of Physics MCQ Edition [Volume 2]
Exam
Concepts Of Physics MCQ Edition [Volume 2]
Subject
Physics
Chapter
The Nucleus

Concepts Of Physics MCQ Edition [Volume 2] · Physics · The Nucleus

A sample containing radioactive ^ 131 I with a half-life of 8.0...

A sample containing radioactive ^{131}\text{I}withahalf−lifeofwith a half-life of8.0 \text{ days}hasaninitialactivityofhas an initial activity of20 \mu\text{Ci}atatt = 0.Findthedecayconstantofthesampleat. Find the decay constant of the sample att = 4.0 \text{ days}.

Options

  1. A2.0×10−6 s−12.0 \times 10^{-6} \text{ s}^{-1}
  2. B0.69×10−6 s−10.69 \times 10^{-6} \text{ s}^{-1}
  3. C1.0×10−6 s−11.0 \times 10^{-6} \text{ s}^{-1}
  4. D1.4×10−6 s−11.4 \times 10^{-6} \text{ s}^{-1}

Correct answer

C. 1.0×10−6 s−11.0 \times 10^{-6} \text{ s}^{-1}

Step-by-step solution

The decay constant λ\lambda of a radioactive substance is a characteristic property of the nucleus and is independent of time and the amount of substance present.

λ=ln⁡2T1/2\lambda = \dfrac{\ln 2}{T_{1/2}}

Given T1/2=8.0 days=8.0×24×60×60 s=691200 sT_{1/2} = 8.0 \text{ days} = 8.0 \times 24 \times 60 \times 60 \text{ s} = 691200 \text{ s}.

λ=0.693691200 s−1≈1.0×10−6 s−1\lambda = \dfrac{0.693}{691200} \text{ s}^{-1} \approx 1.0 \times 10^{-6} \text{ s}^{-1}.
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